Verifiable Knowledge Expansion through Retrieval-Grounded Formal Concept Analysis
Authors: Yujin Yang, Heejung Lee
Organizations: Hanyang University Seoul, Korea
Abstract
Ontology construction requires deciding which objects, attributes, and structural relations should be accepted as valid knowledge. Language models can propose such structures from text, but their outputs can still be unsupported or inconsistent. This paper proposes a retrieval-augmented small language model (SLM) framework that uses formal concept analysis (FCA) as a symbolic verification loop for knowledge expansion. Starting from seed attributes, FCA proposes implications over a growing formal context. A retrieval-grounded SLM oracle then validates each implication or returns a counterexample. The oracle also supports incidence judgments, consistency checks, and attribute proposals, making accepted implications, counterexamples, contradictions, and corrections inspectable. In a rare ataxia setting constructed from Orphadata resources, retrieval-grounded 10-seed runs obtain relation F1 of 0.29-0.52 and closure-based implication F1 of 0.22-0.30. Larger seed sets increase the number of evaluated implications and often improve implication F1. The lower implication scores reflect a stricter evaluation of derived implications, where one missed or extra relation can affect several implication judgments. Ablations show that incidence judgments in a fixed object-attribute setting can improve closure-based implication scores. However, identifying positive object-attribute pairs remains difficult even when the candidate objects and attributes are fixed.
Ontology learning from text remains challenging despite significant progress in Large Language Models (LLMs), which can hallucinate domain terms, produce inconsistent formats, and favor hierarchical over associative relations. In the LLMs4OL 2026 Challenge, we address both the End-to-End Flagship Task (Task A) and Ontology Extension Reuse Task (Task B) using an offline retrieval-augmented few-shot prompting pipeline. Our system employs Qwen2.5-14B-Instruct with all-MiniLM-L6-v2 for demonstration retrieval, selecting the top-5 examples for Task A and top-2 for Task B. A left-truncated context-windowing strategy preserves task instructions within long prompts. For Task B, generated triples undergo deterministic vocabulary-constrained filtering, retaining triples when at least one endpoint belongs to the sample's closed term/type vocabulary and removing duplicates of the initial ontology. The approach achieves Semantic Graph Similarity of 0.8692, Term-Typing F1 of 0.9200, and Taxonomy Discovery F1 of 0.8540 on Task B, while Task A achieves 0.7416 Semantic Graph Similarity. However, no non-taxonomic relations are extracted, highlighting limitations of closed, taxonomy-oriented relation vocabularies.
Grounded claim factuality checking is important for large language model (LLM) applications such as retrieval-augmented generation, as it helps users assess the correctness of generated outputs. Existing metrics using entailment classifiers require dataset-specific threshold tuning, while LLM-based approaches often use direct prompting, which underutilises the reasoning capabilities of LLMs. We address this by formulating grounded claim factuality checking as a true/false reading comprehension task and prompting LLMs with explicit test-taking strategies for efficient reasoning. Our method reduces token usage by over 80% compared to unguided open-ended reasoning, and achieves competitive performance to more expensive alternatives across two factuality benchmarks, setting a new state of the art on one. To further reduce inference cost, we train small language models (SLMs) to replace LLMs in the checking pipeline. Using supervised fine-tuning (SFT) and a self-revision mechanism, the SLMs learn to improve their factuality judgements. Experimental results show that the resulting SLMs perform on par with strong baselines, combining low inference costs with generating supporting rationales to support interpretability. Code and datasets will be released upon acceptance.
Language models exhibit fundamental limitations -- hallucination, brittleness, and lack of formal grounding -- that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investigate whether formal domain ontologies can enhance language model reliability through retrieval-augmented generation. Using mathematics as proof of concept, I implement a neuro-symbolic pipeline leveraging the OpenMath ontology with hybrid retrieval and cross-encoder reranking to inject relevant definitions into model prompts. Evaluation on the MATH benchmark with three open-source models reveals that ontology-guided context improves performance when retrieval quality is high, but irrelevant context actively degrades it -- highlighting both the promise and challenges of neuro-symbolic approaches.